Linear preserver of n × 1 Ferrers vectors

Let A = [ a ij ] m × n be an m × n matrix of zeros and ones. The matrix A is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero (1,1)-entry. We characterize all linear maps perserving the set of n × 1 Ferrers vectors over the binary Boolean semiring and over the Boolean ring ℤ 2 . Also, we have achieved the number of these linear maps in each case.